solve the following word problem. fish is swimming at negative 10.8 m, or 10.8 m below sea level. every 2 minutes it descends another 1.5 m. how long would it take for the fish to read a depth of -37.8 m? show your work and write a sentence to explain what your answer means.
To solve this problem, we can use a simple equation to calculate the time it would take for the fish to reach a depth of -37.8 m:
Depth = Initial Depth + (Rate × Time)
where:
Initial Depth = -10.8 m
Rate = -1.5 m/2 minutes (as the fish descends another 1.5 m every 2 minutes)
Depth = -37.8 m
Let's substitute the values into the equation:
-37.8 m = -10.8 m + (-1.5 m/2 min) × Time
First, let's simplify the equation:
-37.8 m + 10.8 m = (-1.5 m/2 min) × Time
-27 m = (-1.5 m/2 min) × Time
Next, let's solve for Time by dividing both sides of the equation by (-1.5 m/2 min):
Time = (-27 m) / (-1.5 m/2 min)
Time = (2 min/(-1.5 m)) × (-27 m)
Time = (-2/1.5) × 27
Time ≈ -36 minutes
So, it would take approximately 36 minutes for the fish to reach a depth of -37.8 m.
This negative value indicates that the fish is descending below 0 (sea level). Therefore, the sentence explaining the answer would be:
"The fish would take approximately 36 minutes to descend to a depth of -37.8 m, which is 37.8 m below sea level."
To solve this word problem, we need to find out how many times the fish descends by 1.5 m until it reaches a depth of -37.8 m.
Let's set up an equation to represent this situation:
Starting Depth: -10.8 m
Target Depth: -37.8 m
Rate of Descent per 2 minutes: 1.5 m
Let's denote the number of times the fish descends by "n".
After n descents of 1.5 m, the total depth change would be 1.5m x n, which should equal the target depth of -37.8 m.
1.5n = -37.8
Now divide both sides of the equation by 1.5:
n = -37.8 / 1.5
n = -25.2
Since the number of descents can't be negative, we would consider the absolute value of n.
|n| = 25.2
Therefore, it would take the fish approximately 25 descents of 1.5 m each (over 50 minutes) to reach a depth of -37.8 m.
In simpler terms, it would take the fish around 50 minutes to dive down about 37.8 meters below sea level.
To find out how long it would take for the fish to reach a depth of -37.8 m, we need to divide the change in depth by the descent rate.
Change in depth = -37.8 m - (-10.8 m) = -37.8 m + 10.8 m = -27 m
Descent rate = 1.5 m/2 minutes = 0.75 m/minute
Time = Change in depth / Descent rate = -27 m / 0.75 m/min = -36 minutes
Since time cannot be negative, we can conclude that it would take the fish 36 minutes to reach a depth of -37.8 m.
Explanation: The fish is swimming at a depth of -10.8 m and descends 1.5 m every 2 minutes. To reach a depth of -37.8 m, the fish would need to descend an additional 27 m. At a descent rate of 0.75 m/minute, it would take the fish 36 minutes to reach that depth.